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Cross-layer Energy Analysis of Multi-hop WirelessSensor Networks

Jussi Haapola, Zach Shelby, Carlos Pomalaza-Raez and Petri Mahonen∗

{jhaapola,zdshelby,carlos}@ee.oulu.fi, [email protected], University of Oulu, Finland P.O. Box 4500 FIN-90014, University of Oulu, Finland

∗Aachen University, RWTH, Institute of Wireless Networks Kackertstraße 9, D-52072 Aachen, Germany

Abstract— In this paper, we propose a detailed energysurvey of the physical, data link, and network layerby analytical techniques. We also show the impact ofregular sleep periods on node energy consumption andpresent a comparison analysis of single-hop vs. multi-hopcommunications in the energy realm. A detailed energyexpenditure analysis of not only the physical layer but alsothe link and network layer provides a basis for developingnew energy efficient wireless sensor networks. Regular,coordinated sleeping extends the lifetime of sensor nodes,but systems can only benefit from sleeping in terms oftransmitted packets if the data arrival rate to the systemis low. Energy efficiency is the driving motivation for it canbe considered the most important factor for wireless sensornetworks because of the power constraints set by batteryoperation. Radio solutions in the lower ISM bands areattractive because of their relatively easy implementationand low power consumption. However, the data rates ofthese commercial radios are also relatively low, limitingtransmittable frame sizes to a few tens of octets alongwith strict duty cycle requirements. From the analysis weextract key parameters of selected MAC protocols andshow that some traditional mechanisms, such as binaryexponential backoff, have some inherent problems. We alsoargue that single-hop communications has up to 40% lowerenergy consumption than multi-hop forwarding within thefeasible transmission distances of an ISM radio.

Index Terms—Energy efficiency, Wireless sensor net-works, Medium access control (MAC) protocols, Multihopcommunications

I. INTRODUCTION

Sensor network applications have recently become ofsignificant interest due to cheap single-chip transceiversand microcontrollers. Sensor nodes are usually batteryoperated and their operational lifetime should be max-imized, hence energy consumption is a crucial issue.Many single-chip transceivers and therefore sensor net-works are expected to operate using radios like the RFMTR1000 [1], or its European versions all of which workin ISM bands. Regulations in many countries impose

a duty cycle [2], [3], which is normally 10% for the434MHz band and 1% for the 868MHz band. The dutycycle is defined as the ratio, expressed as a percentage,of the maximum transmitter on-time, relative to a onehour period. When a sensor network is expected to workcontinuously, this duty cycle has to be taken into accountand it can affect the energy efficiency of a network.

In this paper we perform cross-layer analysis by pre-senting topology, medium access control (MAC) and ra-dio transceiver energy consumption models that work inunison. The linear topology model represents a commonnetwork after network layer route discovery has beenaccomplished. We use an energy consumption model forthe transmission and reception of MAC frames originallypresented in [4], develop a coordinated sleep groupenergy consumption model, and analytically investigatethe effect of sleep on sensor networks using three MACprotocols. From the analysis we show that althoughin an ideal scenario multi-hop communications performbetter than single-hop communications, realistic energymodels and especially the MAC protocol design havea significant impact. We propose a multi-group sleepmodel for our nanoMAC protocol, and show that reg-ular sleep periods have a significant, energy reducingimpact on node energy consumption with low trafficrates. The radio transceiver energy model takes intoaccount several important radio parameters and we usethe RFM TR1000 and RFM radio designers guide [5] forrealistic transceiver parameters. The main metric usedis absolute energy consumption per useful transmittedbit. This means only the MAC or the network protocoldata unit (PDU) will be considered and all the othercommunicated bits, headers, control frames, preambles,etc. are considered as overhead.

The rest of the paper is organized as follows. Somerelated work is discussed in Section II and in SectionIII we look at the radio propagation energy model.Section IV presents the network topology and energy

analysis without medium access control. In Section V,we briefly look at nonpersistent CSMA and S-MAC,and then give an introduction to a low-power sensorMAC protocol called nanoMAC. Section VI presentsenergy consumption models for the transmission andreception of data and Section VII deals with regular sleepperiods for nanoMAC and presents the worst-case energyconsumption results and the energy savings achievedby regular sleeping. Section VIII addresses the single-hop vs. multihop problem and conclusions are drawn inSection IX.

II. RELATED WORK

The radio model and physical layer characteristics inthis paper are based on the original work from [6]–[8].In [6] optimal transmittable packet sizes are discussedin respect to energy efficiency over single hops. Anenergy consumption model is presented and optimalpacket payload sizes for various channel bit error rates(BER) and coding schemes are determined. In [7] and[8] a linear radio model is presented as seen in Fig. 1for multihop analysis. The latter also presents an optimalhop distance characteristic for multihop communicationswhich is a function of radio parameters and heavilydependent on the individual radio used.

During the past few years there has been some lit-erature on energy efficient MAC protocols specificallyfor use with sensor networks [9]–[11]. However, suchprotocols are usually modifications from traditional adhoc networking and have some inherent flaws for sensornetworks. The PAMAS [9] protocol was one of thefirst attempts to reduce unnecessary power consumptionby turning overhearing nodes to sleep. The protocolhowever needs a separate control channel for coordi-nation and avoiding overhearing. It also does not takeinto account idle listening in any way, which accountsfor a large portion of energy consumption. The sensorMAC (S-MAC) [10] is a protocol designed for sensornetworks and its prime functionality is to reduce idlelistening. S-MAC’s foundations lie on IEEE802.11 [12]and MACAW [13], which is the basis of IEEE802.11.They both implement carrier sense multiple access withcollision avoidance (CSMA/CA), a four-way RTS-CTS-Data-ACK handshake using binary exponential backoffand other similar functionality. S-MAC also implementsa regular sleep period and a special synchronizationscheme to reduce idle listening and maintaining globalconnectivity. The method is called virtual clustering,where irregular SYNC messages urge, but do not enforcea common schedule. Even though S-MAC outperforms

Sink d

R = nd

... n n-1 3 2 1

N Sensor nodes

Fig. 1. Simple linear sensor network.

IEEE802.11-like protocols in the energy perspective itis still a traditional ad hoc protocol in many ways. Thetimeout MAC (T-MAC) [11] is an evolution of S-MACinto even lower energy consumption by not only reduc-ing idle listening, but also making the active periods ofthe protocol dynamic. The data communications in T-MAC is highly bursty, minimizing the active time andforcing the bursty periods to operate in a very highcontention environment. It shares many of the features ofS-MAC but achieves superior performance over S-MACin certain cases.

There has been a lot of research on efficient wirelesssensor network topologies that include LEACH [14],SPIN [15], data funnelling [16] and directed diffusion[17]. Each of them suggest a method of energy efficientnetwork formation. LEACH builds dynamic clusters toensure that most nodes need to transmit only smalldistances and SPIN sensor nodes advertise data theyhave so that only interested nodes can ask for the data.Data funnelling creates sensing areas with border nodesso that data from an area is gathered to border nodesthat find and use a multi-hop path to the sink nodeand in directed diffusion the sink node broadcasts whatdata it is interested in and build gradients to the nodeswho have the data of interest. All of the mentionedprotocols are data-centric, which is a good assumptionfor sensor networks and implies that the data itself isthe key element in the network, not the sensor nodesthat sent it. Of the mentioned protocols, SPIN, datafunnelling, and directed diffusion can be modelled withthe linear network shown in Fig. 1 in steady state.Directed diffusion employs redundant paths for routingdata infrequently causing some compatibility problemswith the linear topology. In this work, we take intoaccount the MAC protocol contention of not only thelinear network but the whole network surrounding thepath of the linear network. Fig. 2 illustrates this andtherefore, the redundant paths can be modelled as anexternal traffic load affecting the contention process andconsuming energy.

The closest related work to our paper was presented in

Sink

Linear path

Fig. 2. Simple linear sensor network.

[18]. The paper is a MAC–routing protocol cross layerstudy for ad hoc communication networks. Although thework is on ad hoc protocols and does not take energy us-age into account it shows the importance of consideringdifferent layer protocols when designing a new protocol.This is demonstrated with Ad Hoc On Demand DistanceVector (AODV) routing and IEEE802.11. AODV is de-signed to work specifically on top of the IEEE802.11MAC protocol and achieves its best performance withthat MAC and also has the best overall throughput of theMAC–routing protocol combinations presented in [18].

III. RADIO POWER CONSUMPTION

Power consumption models of the radio in embeddeddevices must take both transceiver and start-up powerconsumption into account along with an accurate modelof the amplifier. The latter actually becomes dominantwith small packet sizes and long transition times toreceive mode because of frequency synthesizer settle-down time. In [6] a model for radio power consumptionis given for energy per bit (eb) as

eb = etx + erx +Edec

ι, (1)

where etx and erx are the transmitter and receiver powerconsumptions per bit, respectively, Edec is the energy re-quired for decoding a packet, and ι is the payload lengthin bits. The encoding of data is assumed to be negligible.This model takes the energy needed to transmit a framefrom a transmitter to a receiver over a single hop intoaccount. In [6] the model was used over a single hopto optimize frame sizes and coding techniques. In thispaper we extend the model for multihop scenarios andwith different traffic models. It is then extended later inthe paper to analyze multihop MAC efficiency.

The term etx from (1) with optimal power control can

Fig. 3. Radio energy consumption model.

be represented as

etx = ete + etadα, (2)

where ete is the power consumption of the transmitterelectronics, eta is the consumption of the transmit am-plifier, d is the transmission distance, and α the path lossexponent. Often in the literature generic approximationsare used for these terms. However, an explicit expressionfor eta has been presented in [8] as

eta =( SN )r(NFRx)(N0)(BW )(4π

λ )α

(Gant)(ηamp)(Rbit)(3)

where ( SN )r is the desired signal to noise ratio at thereceiver’s demodulator, NFRx is the receiver noise figure,N0 is the thermal noise floor in a 1 Hz bandwidth, BWis the channel noise bandwidth, λ is the wavelength inmeters, α is the path loss exponent, Gant is the antennagain, ηamp is the transmitter efficiency, and Rbit is the rawchannel rate in bits per second. This expression for eta

can be used for those cases where a particular hardwareconfiguration is being considered as in this paper. Inthe same paper the authors have shown that an optimalmultihop distance, the characteristic distance dchar canbe defined as

dchar = α

√ete + ere

eta(α− 1). (4)

For the parameters shown in Table II the characteristicdistance is 31.5 meters with a BER of 10−4 assumingnon-coherent FSK modulation.

IV. MULTIHOP POWER CONSUMPTION

In this section an analytical model for multihop com-munications is introduced that takes detailed overheadsinto account. A linear model is used with variable spac-ing between nodes assuming a sink node that collectsdata and is not energy dependent. No medium accesscontrol is assumed. Energy per bit, energy efficiency andtotal energy are derived for various traffic cases and nodedistributions.

A similar analysis can be made as in [19] by extending(1) to take the linear multihop scenario shown in Figure 1into account, assuming optimal power control. Insteadof total power derived in [19] we can derive multihopenergy per useful bit from (1) as

eb = (n(ete + eta(d)α) + (n− 1)ere)(1 +(β + τ)

ι)

+nEst + (n− 1)(Esr + Edec)

ι, (5)

where ete is the energy per bit needed by the transmitterelectronics, ere for the receiver electronics, Est andEsr are startup energies, eta is the power needed tosuccessfully transmit one bit over one meter, α is thepath loss exponent, β is the preamble length, τ is thecoding overhead and n is the number of hops.

For this same topology we can also calculate thetotal energy consumed in the network. Using the samenotation as in (5) total multihop energy consumption is

EMH = n(k(ete + eta(d)α) + Est)

+ (n− 1)(ker + Esr + Edec), (6)

where k is the number of bits transmitted. The analysisused to this point has taken an unrealistic traffic assump-tion into account, that is, only node n (furthest from thesink) transmits data. This was necessary for calculatingenergy per bit and energy efficiency, which are frame-centric metrics. However, in most useful scenarios allnodes will transmit data. We can take that into account byassuming that all nodes have a single frame to transmittowards the sink. Total energy for this scenario is

EallMH =

n(n+ 1)

2(k(ete + eta(d)α)) + Est)

+n(n− 1)

2(ker + Esr + Edec). (7)

We can compare this multihop case to the single-hopcase where each node transmits its frame directly to thesink node, that is, no forwarding is performed. This iscalculated as

EallSH =

n∑

i=1

(k(ete + eta(id)α) + Est). (8)

In addition, we can calculate energy consumption froma node-centric point of view, that is, how much powerdoes a particular node n consume. This is useful whenbalancing the power consumed in packet forwarding. Forthe multihop case this is calculated as

EallMH(i) = (n− i+ 1)(k(ete + eta(d)α) + Est)

+ (n− i)(ker + Esr + Edec), (9)

and for the single-hop case as

EallSH(i) = k(ete + eta(id)α) + Est. (10)

V. MAC PROTOCOLS

In this section the MAC protocols to be used for en-ergy analysis in this paper, namely nonpersistent CSMA,S-MAC and nanoMAC, will be described. NonpersitentCSMA is a well known, relatively well performingMAC protocol in almost any scenario. It gives worst-case energy performance that any sensor MAC proto-col should outperform. S-MAC is the current sensorMAC benchmark protocol which is used to highlightsome of the faults of traditionally designed sensor MACprotocols. We compare these to nanoMAC, a protocoldesigned to operate in a sensor networking environment.

A. Nonpersistent CSMA

Carrier sense multiple access (CSMA) was originallypresented in [20] and has been widely referenced af-terwards. The reason for using the energy consumptionmodel with nonpersistent CSMA (np-CSMA) in this pa-per is that np-CSMA is a protocol which performs quitewell under most circumstances, even though theoreticallyit is an unstable protocol. It also functions as a worst-case model for sensor MAC protocols. When a nodeusing np-CSMA has data to send it first uses carriersensing (CS) to sense the channel. If the channel is foundvacant for the whole duration of the CS the node sendsthe data, otherwise it does not persist on sensing thechannel, but chooses a random time in the future to doCS again. Once the data has been sent, np-CSMA waitsfor an acknowledgement (ACK) frame from the intendedrecipient and if the ACK is received before a timeout, thedata is known to be successfully received. Otherwise, thedata has to be retransmitted at a later time. As a deviationfrom the original paper, the ACK frame is transmitted onthe same channel as data.

B. S-MAC

The S-MAC [10] operation and frame is divided intotwo periods; the active period and the sleep period.During the sleep period all nodes that share the sameschedule sleep and save energy. The sleep period isusually several times longer than the active period andin our analysis we use 1 second sleep times. The activeperiod also consists of two subperiods; the listen forSYNC packet period and the listen for RTS period.

Arrive

Backoff Attempt Success

(1-P b )P ers , Transmit RTS

(1-P s ) , Collision, go to backoff

(1-P c ) or P c (1-P ers ), Channel detected busy,

stay in backoff

P c P ers , Channel detected vacant, transmit RTS

P s , Transmit data, receive ACK

Carrier Sense

P b or (1-P b )(1-P ers ), Refrain from transmission

Fig. 4. NanoMAC TX energy model.

Nodes listen for a SYNC packet in every frame and theSYNC packet is transmitted by a device infrequently toachieve and maintain virtual clustering. In the listen forRTS part the nodes can communicate using a CSMA/CAchannel access method with binary exponential backoff.S-MAC also implements a technique called messagepassing which means that if the networks layer hasa larger than MPDU packet to transmit, S-MAC cansplit up the packet into smaller MPDU sized piecesand transmit them as a burst of consecutive Data–ACKframes. Overhearing nodes sleep during the data transfer.The active period is 300 ms in our analysis and listenfor RTS is 115 ms.

C. NanoMAC

Because CSMA/CA is a powerful tool for medium ac-cess control, the nanoMAC protocol also implements thisfeature which has been discussed in detail in [21], [22].Briefly described, nanoMAC is a p-nonpersistent, i.e.,with probability p, the protocol will act as nonpersistentand with probability 1− p the protocol will refrain fromsending even before CS and schedule a new time for CS.Nodes contending for the channel do not constantly listenfor the channel, but sleep until the contention windowvalue is low. Then the node wakes up to sense if thechannel is busy for a short but high confidence periodbefore transmitting if the channel is detected vacant. Thisfeature makes the carrier sensing time short, even thoughthe backoff mechanism is binary exponential and savesenergy. In the request-to-send/clear-to-send (RTS/CTS)frames nanoMAC does virtual carrier sensing in additionto informing overhearing nodes of the time they arerequired to refrain from transmission. Virtual carriersensing enables overhearing nodes to sleep during thatperiod. Unlike S-MAC, IEEE MAC addresses are sup-

ported as well as sleep information for virtual clusteringand the number of data frames to be transmitted are alsoincluded in the RTS and CTS frames.

The data frames carry only temporary, short, randomaddresses to minimize the data frame overhead. With oneRTS/CTS reservation a maximum of 10 data frames canbe transmitted using a frame train ideology The ideais similar to message passing in S-MAC, but it is adefault characteristic in nanoMAC and the data framesare acknowledged by a single, common ACK frame thathas a separate acknowledgement bit reserved for eachdata frame. The ACK frame is therefore an acknowledge-ment/negative acknowledgement (ACK/NACK) combi-nation. In this way only the corrupted frames need to beretransmitted and not the whole packet. When forwarderror correction (FEC) methods are not used, the frametrain method promises to be efficient. If FEC should beused, frames can be made longer. When best utilised,nanoMAC has low overhead even with low data-rate,small frame size applications. For example, a data-rateof 19.2 kbps with 4B/6B encoding provides a 12.8 kbpsdata-rate for the MAC layer. According to [6] a frameof 41 octets with a BER of 5× 10−4 is close to optimalenergy efficiency. With 41 octet data frames and 18octet RTS/CTS/ACK frames the MPDU-to-packet ratiois ∼75% while for np-CSMA the same efficiency witha 41 octet data frame and 15 octet ACK is ∼44%. ForS-MAC, the data frame is 43 octets and control framesare 10 octets and produce an MPDU-to-packet ratio of∼64% with 350 octet MPDU and message passing.

VI. ENERGY CONSUMPTION MODEL

In this section we briefly describe the theoreticalenergy consumption of MAC protocols and the underly-ing physical layer. The energy consumption model was

presented by the authors in [4] and consist of energyconsumed in the transmission and reception of data, butwe have extended our analysis in all directions. Themodel used was originally presented in [23] for a delayanalysis of the FAMA-NTR protocol, but we have mod-ified it to be used for energy consumption calculationsby investigating the probabilities of transitions from onestate to another state and the related times consumedin transmit, receive, idle and sleep. Usually, in ISMtransceivers, receive and idle modes can be consideredas a single mode or the difference is marginal.

The energy consumption model for transmission canbe found from Fig. 4. There are four different states:Arrive, Backoff, Attempt and Success. The Arrive stateis the entry point to the system for a node gettingnew data to transmit. To calculate the average energyconsumption, we solve a system of equations implied byFig. 4. Let ETX equal the expected energy consumptionby a node with new data at the Arrive state until thenode reaches the Success state. Let E(A) equal theaverage energy consumption on each visit by the nodeto the Attempt state, and let E(B) equal the energyconsumption on each visit to the Backoff state. Theaverage energy consumption upon transmission from thepoint of packet arrival from the upper layer to the pointof receiving an ACK frame is

ETX =TCSMRX + Pb

(Tbb +

Tr2

)MSlp + PbE(B) (11)

+(1− Pb)(1− Pers)

(Tbp +

Tr2

)MSlp

+(1− Pb)PersE(A) + (1− Pb)Pers(Tpr + RTS)MTX

+(1− Pb)(1− Pers)E(B).

• MTX, MRX, and MSlp are transceiver modes TX, RX,and sleep, respectively,

• TCS is the time required for carrier sensing,• Tbb and Tbp are incremented and un-incremented

backoff times, respectively,• Pb is the probability of finding channel busy during

CS,• Tr/2 is the average random delay,• Pers is the non-persistence value of nanoMAC, and• Tpr and RTS are times to transmit a preamble and

an RTS frame, respectively.From E(B) and E(A) we make the same analysis as

from the Arrive state and solve a system of equations.The term E(A) gives a constraint: the probability of nocollision with retransmit RTS Pc 6= 0 and probability ofsuccessful data transmission Ps 6= 0→ G ∈ ]0,∞[.

Idle

( 1-P s ), No valid RTS

received, stay in idle

Reply

Received

P s , Valid RTS received (1-P

senh ), Collision

during CTS

P senh , Receive data packet

Fig. 5. NanoMAC RX energy model.

For np-CSMA and S-MAC a state machine similar toFig. 4 can be drawn but with different probabilities andvalues. The transmit energy consumption of np-CSMAand S-MAC is of the format ETX = γ + σE(B) + φ +(1 − σ)E(A), where γ and φ are sums of products ofprobabilities, time, and transceiver modes and σ is aprobability based on the value of the congestion window.

The reception energy consumption model of a packetcan be found from Fig. 5 and the average receive energyconsumption ERX from listening for a transmission todetecting and receiving a valid packet and being theproper destination can be found to be

ERX = E(I) = (µ+ Psθ)(PsPsenh)−1. (12)

• E(I) is the time incurred in each visit to state Idle,• µ and θ are functions of different probabilities

multiplied by times spent in different transceivermodes,

• Ps and Psenh are the probabilities of no collisionduring RTS or CTS, respectively.

For reception, the constraint PsPsenh > 0 → G < ∞is introduced. The energy consumption for np-CSMAand S-MAC on reception can be calculated using Fig. 5and replacing the probabilities, times, and transceivermodes with appropriate ones. The average energy peruseful bit on transmission and reception of the protocolsis depicted in Fig. 6. From the figure we can see that np-CSMA transmission energy consumption is the highest,as expected and about 40% higher than with nanoMAC,but only 7% higher than with S-MAC. Surprisingly,S-MAC receive energy consumption is the highest of

10−3 10−2 10−1 100 101 102 103 1041

2

3

4

5

6

7

8

9

10x 10−6

Normalised traffic G(Erlang)

Abs

olut

e en

ergy

con

sum

ptio

n E

(J) p

er s

ucce

ssfu

l use

ful b

it

TX P0.01

nanoMACTX P

0.1 nanoMAC

TX P1.0

nanoMAC

TX np−CSMATX S−MACRX np−CSMARX nanoMACRX S−MAC

Fig. 6. Transmission and reception energy consumption per MPDUbit.

the three protocols. This is due to three factors: Inthe calculations done in Matlab, artificially small ACKframes of 1 octet were used for np-CSMA. This is dueto the fact that longer ACK frames for np-CSMA wouldlead to a deadlock situation in the worst-case energyconsumption scenario presented in the next chapter.Secondly, binary exponential backoff causes S-MAC andalso np-CSMA to spend on the average a relatively longtime in transceiver RX mode before data transmission.Third, S-MAC has a cyclic listen for SYNC period,in which the transceiver has to be in RX mode. Noactual data can be communicated during that time, so apotential transmitter has to spend extra time in RX mode.In nanoMAC the synchronisation is handled in RTS, CTSand ACK frames, so no extra listening is required pertransmitted data packet. NanoMAC reception thereforeconsumes less than 2

5 of the energy in reception peruseful bit compared to S-MAC.

VII. REGULAR SLEEP PERIODS

We can now calculate the average maximum powerconsumption for a node using the European version ofthe RFM TR1000, the 433.92 MHz ISM transceiverRFM TR3000 and nanoMAC with and without sleepperiods or np-CSMA without sleep. Because S-MAC hasan inherent sleep cycle, we use a similar model. The 433MHz band has a legal duty cycle of 10% implying thata node is allowed to transmit only one tenth of its activetime, i.e., whenever a node sends a packet to some other

TABLE ICOMMUNICATION PACKET SIZES

Parameter (octets) nanoMAC CSMA S-MACArrival packet size, Apkt 350 25 350Packet on the channel, Cpkt 507.25 49 627Cpkt; Sender transmitter, STX 464.25 44.5 478.5Cpkt; Receiver transmitter, RTX 43 4.5 148.5

node it has to refrain from transmission for a period of9 times the time it took to transmit the packet. The dataarrival rate to the system is Poisson distributed and fromTable I we can see relevant parameters for the data packetcommunication.

We consider a maximal usage case in which a node(i)transmits a packet as often as possible, without bufferingand it is the recipient for all of the packets sent in thechannel, except the one packet it transmits.

A. Worst-case Scenario

A node can transmit a packet every Ttp seconds,

Ttp =STX

RdCd+ MAX(n)

(RTX

RdCd

)Gmod, (13)

where Rd is the data rate (bps), Cd the duty cycle, and nthe number of packets addressed to node(i) that node(i)receives during a wait between packet transmissions Ttp.Gmod is the average, normalised traffic with a limit thatwhen G > 1→ Gmod = 1. The value of MAX(n) can bedefined as the maximum number possible (n) in a Ttp atG = 1 by

MAX(n) =

(STX

Cd(Cpkt + Tproc)− 1

)(1− RTX

Cd (Cpkt + Tproc)

)−1

(14)

The processing delay Tproc, is expressed in bits. Weuse a 1 octet ACK for np-CSMA because should oneuse a 15 octet long ACK frame (ACK frame withIEEE sender/recipient MAC addresses) for np-CSMA,the value of MAX(n) would take negative values, i.e., adeadlock in which a node first transmits a data frame andthen by sending ACK frames corresponding to receiveddata frames would consume all the time available fornew data transmissions.

In nanoMAC RTS, CTS and ACK frames, the sleepfield is divided into two parts:• Sleep Group: This field announces the sleep group

the node is currently following. There are fourdifferent sleep groups: SG 00 with no sleep periods,SG 01 in which nodes wake-up every 0.4 s, SG 10,

10−3 10−2 10−1 100 101 102 103 1040

0.2

0.4

0.6

0.8

1

1.2

x 10−4

Normalised traffic G(Erlang)Abs

olut

e en

ergy

con

sum

ptio

n E

(J) p

er u

sefu

l bit

trans

mitt

ed b

y de

vice

(i) w

ith s

leep

gro

ups

nanoMAC P1 no sleep

nanoMAC P1 SG 01

nanoMAC P1 SG 10

nanoMAC P1 SG 11

np−CSMAS−MAC

Fig. 7. Worst-case energy consumption per MPDU bit.

with 0.96 s wake-ups, and SG 11, with 1.6 s wake-ups.

• Next Wake-Up: This field indicates the next timethe node will be awake for communication. Theresolution of the field depends on the Sleep Group.

After wake-up the nodes stay awake for an active periodplus a period {0 − Cpkt}. Any node overhearing oneof the control frames can calculate the times when thesource node will be active. An overhearing node cansynchronize with the overheard frame source. For mutualsynchronization issues, after a 9.6 s synch. period, a nodefirst transmitting a frame will send a long preamble sothat every overhearing node in every Sleep Group cansynchronize their relative times to it. Every node keepsthe schedules of all its immediate neighbors, or at leastthe schedules of the neighbors it wishes to communicatewith.

B. Energy Consumption with Sleep Groups

When considering sleep groups, we assume that thesender and recipient are synchronized in time so thatwhen the sender transmits, the recipient is awake toreceive data. Because the transmitter and receiver aresynchronized in time, sleeping mainly reduces idle lis-tening. Sleeping also increases the traffic offered to thechannel because some arrivals occur during the sleepperiod and every new arrival can be allocated for a newnode to satisfy the Poisson distribution. The total worst-

TABLE IIRADIO PARAMETERS

Parameter ValueTransmitter circuitry, ete 1.066 µJ/bitReceiver circuitry, ere 0.533 µJ/bitSNR at the receiver, ( S

N)r 40 dB

Receiver noise figure, NFRx 10 dBThermal noise floor, N0 4.17 ∗ 10−21 JBandwidth, BW 19200 HzWavelength, λ 0.327 mPath loss exponent, α 2.5Antenna gain, Gant -10 dBTransmitter efficiency, ηamp 0.2Raw bit rate, Rbit 19200 bits/sSleep mode energy 120 pJ/bit

case energy consumption with sleep is found to be

Eslp =mTawGimod

Ttp

(1

Cpkt− 1

RdTtp

)(1− Apkt

RdTtpGinc

)ERX (15)

+ETX +m(Twup − Taw)

ApktMSlp +

mTaw(1−Gimod)

TtpTidleRX

MidleRX

Apkt

Here m = Ttp/Twup is the number of wake ups duringTtp, Twup the wake up period defined by sleep groups, Taw

the period a node is awake, Gimod the increased trafficoffered to the channel with a maximum value of 1, andGinc the increased traffic.

The radio parameters are listed in Table II and thetotal energy consumption per useful transmitted bit inthe worst-case scenario with and without sleep groupsis depicted in Fig. 7. The behavior of the curves needssome explanation. The high energy consumption per bitat low values of G is explained by the fact that theoffered traffic to the channel is very low and nodesspend most of their time in idle listening. The actualenergy consumed in the transmission of a packet isnegligible compared to the energy consumed in idlelistening between successive data packet transmissions.This behavior is common to all of the MAC protocols weconsider. We can see that the introduction of sleep groupsand S-MAC’s inherent sleep schedule help to compensatefor the idle listening, but it can be seen that one needsat least a 15:1 sleep:awake cycle (nanoMAC SG 11)to keep the energy per useful bit value low. When Gincreases, nanoMAC performs very well for a wide rangeof G, but eventually in extremely high bursts of G theenergy consumption becomes exponentially increasing.NanoMAC accomplishes this by solving most of theproblems of being passive and sleeping. The low energyconsumption trade-off is increased delay as our workin [22] implies (with throughput–delay calculations).

When nodes are passive, the actual traffic offered to thechannel increases as new arrival occur. The contentionis therefore higher and the delay increases rapidly afterG becomes higher than 1. The good performance ofnanoMAC is also due to the fact that overhearing nodessleep for the duration of data transmission as well as forthe duration of the backoff times.

Similar behavior can be seen for S-MAC, but thereis a clear energy consumption minimum seen aroundG = 0.07. This is the point where there is exactlyone data packet arrival per Ttp. When the traffic loadincreases node(i) begins to receive data packets in ad-dition to its own transmissions. Idle time is reduced,but the high energy consumption of receiving increasesenergy consumption. The energy consumption per usefultransmitted bit soon reaches a steady state or a saturationpoint, where extra traffic no longer increases the amountof data node(i) receives per Ttp because Ttp has reachedits maximum value no more traffic can be communicatedin the channel. When the instantaneous traffic offeredto the channel reaches very high values, the numberof collisions effectively block communications on thechannel and energy per useful transmitted bit grows firstlinearly, then exponentially.

The performance of np-CSMA on the other hand isquite interesting, but the behavior is exactly the sameas for S-MAC. At low values of G the performanceof np-CSMA is similar to that of nanoMAC withoutsleep for the same reasons as for nanoMAC. When Gincreases to the point where there is more than onearrival (during Ttp) to the system, the energy consump-tion starts increasing linearly because the number ofreceived packets per Ttp grows linearly. The increase ofreception continues for a while until the channel startsto saturate with data packets. Because of np-CSMA’ssimplicity high instantaneous bursts of traffic lead to arapid increase in energy consumption per useful bit.

The energy saving effect of regular sleeping is mainlywith low values of G. This is because the amount ofidle listening is reduced by a large factor. We expectthat the same energy saving behavior is not limited tothis worst-case scenario, but is applicable whenever Gis low.

VIII. MULTI-HOP ANALYSIS

A. Cross-layer Results

The results presented in this section were collectedusing Matlab. The parameters used are shown in Table II(Fig. 8 has α = 2.3). In addition a 350 byte payload with4B/6B coding is assumed for comparison with results

05

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Tota

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(J) Single−hop

Multihop

Fig. 8. Total energy for the node n transmitting case. This plot showsthe relationship between multihop and single-hop energy efficiency.Single-hop is typically more efficient within the radio’s transmissionrange. The path loss exponent α is 2.3 in this case.

in the next section. Using this model we can comparethe use of single-hop and multi-hop communications inlow-power networks. The real question is whether trans-mit energy or receive and startup energy are dominantfactors, the former favoring the theory that multi-hop isalways more efficient. However, when accurately takingstartup energies and other overheads into account, itcan be shown that in most practical cases single-hoptechniques are preferred for energy efficiency.

The relationship between multi-hop and single-hopenergy efficiency is shown in Fig. 8. Here we can seehow the planes of multi-hop and single-hop intersect.Multi-hop is more efficient with a small number ofhops over larger distances. Past the typical transmissionrange of the radio (around 80 m in this case) single-hopbecomes less efficient because of path loss. In Fig. 9 wecan see how the traffic model affects this intersection.The all nodes transmitting case increases the range underwhich single-hop is more efficient. Note that in bothcases the intersection is beyond the practical range ofthe radio. These results are highly influenced by radioand channel parameters, and thus are meant only to showthe general relationship.

B. Cross-layer Results with Medium Access Control

We use the linear topology of Fig. 1 where N is thetotal number of nodes with uniform optimum spacingd. When using multi-hop, one hop is d and one makesN hops to reach the sink node whereas for single-hop,

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(J)

MultihopSingle hopMultihop (all)Single hop (all)

Fig. 9. Comparison of the node n and all node transmission trafficcases. It can be seen that the crossover point is further in the allnodes transmitting case.

node N transmits the same data for one hop with thedistance Nd. Three different scenarios are investigated:one with perfect sleep scheduling, one with realizablemulti-group sleep scheduling, and one with commonsleep scheduling. In perfect sleep scheduling only thesource and the immediate destination are awake duringany given transmission and there are no overhearingnodes. With multi-group sleep scheduling we use thefour level sleep scheduling presented earlier in the paperand assume that 25% of nodes obey each sleep schedule.Notice that all of the sleep schedules overlap in certainwake periods to keep the network fully connected andall the nodes that are awake during a transmission willoverhear the transmission if they are within the rangeof the transmission. When common sleep scheduling isused we assume that all the n nodes in the linear networkare awake at the same time, so all the nodes withinthe transmission radius will overhear the transmissions.When using the transceiver specific characteristic dis-tance, dchar (31.5 m in this case), we note that the multi-hop communication always outperforms the single-hopstrategy. The phenomenon is independent of the MACprotocol and presents an optimum separation of nodes.However, when the distance, d, is not optimum thesingle-hop communications can outperform the multi-hop strategy. A distance, d, of 10 meters per hop ischosen and the following is observed.

Fig. 10 presents nanoMAC and S-MAC with commonand perfect sleep scheduling. The figures are calculated

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P1 nanoMAC, single−hop, common sleep

P1 nanoMAC, single−hop, perfect sleep

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1 nanoMAC, multi−hop, common sleep

P1 nanoMAC, multi−hop, perfect sleep

S−MAC, multi−hop, common sleepS−MAC, multi−hop, perfect sleep

Fig. 10. NanoMAC and S-MAC with a linear topology, non-optimalspacing.

at G = 0.22 and it is assumed that multi-hop com-munications occur within a longer period in order notto increase the offered traffic due to forwarding. Thereis little difference in energy consumption per useful bitbetween common sleep group and perfect sleeping withCSMA/CA type MAC protocols. The multi-group sleepalgorithm falls in between the two cases. The energyexpenditure of nanoMAC however, is considerably lessthan S-MAC with both single-hop and multi-hop com-munications. Fig. 11 illustrates the behaviour of the mod-ified np-CSMA. It is assumed np-CSMA uses similarsleep scheduling to nanoMAC and the ACK frame lengthis 1 octet. The energy consumption difference of thesleep groups can be observed with MAC protocols likeCSMA where the length of overheard frames are longand the multi-group sleep algorithm provides 10− 20%better performance than common sleeping.

Fig. 12 illustrates the energy consumption behaviorof nanoMAC, np-CSMA, and S-MAC with commonsleep group. The protocols exhibit similar behavior tothat of Figs. 8 and 9 which are calculated withoutmedium access control. The energy difference per usefulbit is almost two orders of magnitude greater when theMAC is taken into account. All of the MAC protocolshave an intersection point with single-hop and multi-hopcommunications, but the intersection point is above thefeasible transmission radius of our transceiver. Therefore,single-hop communications should be preferred when thepath loss is moderate or less. The energy savings can

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it in

a c

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mitt

ing

np−CSMA, perfect sleep, single−hopnp−CSMA, SG 01np−CSMA, common sleepnp−CSMA, perfect sleep, multi−hopnp−CSMA, SG 01np−CSMA, common sleep

Fig. 11. Nonpersistent CSMA with a linear topology and non-optimal spacing.

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up P1 nanoMAC, single−hop

np−CSMA, single−hopS−MAC, single−hopP

1 nanoMAC, multi−hop

np−CSMA, multi−hopS−MAC, multi−hop

Fig. 12. Linear topology for the MAC protocols using commonsleep group and link distances, d of 10 m.

range up to 30− 40% depending on the MAC protocol.and implies that the use of single-hop communicationsis more energy efficient in wireless sensor networks,where the offered traffic is usually low or moderate. Thedifferences in energy consumption between the MACprotocols are high and show the importance of properdesign of a MAC protocol for sensor networks.

IX. CONCLUSIONS

In this paper, we have analytically investigated a cross-layer energy consumption model with realistic radiotransceiver characteristics, three MAC protocols and alinear network model suitable for many sensor networkprotocols in steady state. Based on the analysis we havediscovered many interesting results that relate to single-hop vs. multihop communications and MAC protocolfeatures. Firstly, when a realistic radio model is appliedfor a sensor network, we discovered that with feasibletransmission distances single-hop communications canbe more efficient than multi-hop in the energy perspec-tive. The conditions are the multi-hop hop distances, d,are less than the radio-specific optimal multi-hop trans-mission distance dchar and that the path loss exponent isless than 2.7. Secondly, a well designed sensor MACprotocol has similar behavior to the case where theMAC protocol can be considered ideal; only the absolutevalue energy consumption is higher, on the order of twomagnitudes.

Thirdly, there are some inherent flaws in adaptingexisting ad hoc MAC protocols to sensor networks.Idle listening and overhearing avoidance are importantfactors as already discussed in other publications, suchas [10], [11], but also any listening that is not abso-lutely necessary, like listening for the RTS in S-MAC,decreases the energy performance of a sensor MAC.Binary exponential backoff, where nodes listen for thechannel for the duration of the contention window beforetransmitting also increases energy consumption, espe-cially when the offered traffic to the channel increases.If message passing techniques are used, transmitting anACK frame and the related turnaround times consumea large amount of energy and occupy the channel for alonger time, then ACKs should be combined. Of coursecombining ACK frames make the larger ACK moreimportant and might need methods for ensuring integrity.

It has been shown that introducing regular sleep peri-ods can have a major impact on the energy consumptionof a node, especially with low traffic loads. The lowduty cycle of ISM bands also demands regular sleepperiods. Sleep periods increase the delay, however it canbe justified because of the energy savings. Regular, co-ordinated multi-group sleeping also decreases the energyconsumption in both single-hop and multi-hop commu-nications. This applies to CSMA like protocols where theoverheard frames are long because multi-group sleepinglimits the number of overhearing nodes. The energysaving depends heavily on the MAC protocol used as

well as whether single-hop or multi-hop communicationsis used. From the analysis we can conclude, however thatwith an energy efficiently designed MAC protocol, likenanoMAC, up to 40% energy savings can be achieved byusing single-hop communication within the transmissionrange of a low frequency ISM transceiver.

X. FUTURE WORK

In order to continue the analysis further analyticalresults will be compared with real measurements. Wehave developed nanoMAC on TinyOS for the BerkeleyMICA2 motes and on the CWC’s WIRO sensor platformto make measurements. Also, we have assumed an error-free or nearly error-free (BER 10−4) channel and needto analyze the energy behavior with different bit errorrates. This implies major modifications to the MACenergy model or a switch to Markov chains and afinite number of nodes. Different sensor network trafficmodels influence the energy consumption and the typesof protocols to use, so the definition of traffic modelsother than data-centric nodes to the sink are also needed.Finally, this problem needs to be considered also fromthe transport and application layer. Different schemesfor packet forwarding in sensor networks should becompared using this a similar cross-layer analysis.

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